This article presents the notion of the continuous case of the weighted Tsallis extropy function as an information measure that follows the framework of continuous distribution. We introduce this concept from two perspectives, depending on the extropy and weighted Tsallis entropy. Various examples to illustrate the two perspectives of the weighted Tsallis extropy by examining a few of its characteristics are presented. Some features and stochastic orders of those measures, including the maximum value, are introduced. An alternative depiction of the proposed models concerning the hazard rate function is provided. Furthermore, the order statistics of the weighted Tsallis extropy and their lower bounds are considered. Moreover, the bivariate Tsallis extropy and its weighted version are derived. Non-parametric estimators are also derived for the new measures under cancer-related fatalities in the European Union countries data. Additionally, a pattern recognition comparison between Tsallis extropy and weighted Tsallis extropy is presented.

In this paper, we investigated the estimation and prediction problems based on current record statistics arising from the Weibull distribution. The Weibull model is widely used in industrial reliability, survival analysis, and environmental sciences. Under the assumption that the data represent current records from a two-parameter Weibull distribution with shape parameter $k$ and scale parameter $\lambda$, we derived the new probability density function (PDF) and cumulative distribution function (CDF) of upper and lower current records. After that, a closed-form expression for the moments of upper and lower current records was obtained. Later, the maximum likelihood and Bayesian estimators for the parameters were obtained, along with predictions of future current record values and a predictive interval. Monte Carlo simulation was performed to assess the performance of the proposed estimators under various sample sizes and parameter settings. The methodology was further illustrated using an application to industrial data from Saudi Arabia, demonstrating the practical relevance of Weibull record modeling for reliability and life-testing analysis.